Asymptotic Properties of the Maximum Likelihood Estimator for Stochastic Parabolic Equations with Additive Fractional Brownian Motion

Asymptotic Properties of the Maximum Likelihood Estimator for Stochastic Parabolic Equations with Additive Fractional Brownian Motion

A parameter estimation problem is considered for a diagonalizable stochastic evolution equation using a finite number of the Fourier coefficients of the solution. The equation is driven by additive noise that is white in space and fractional in time with the Hurst parameter H ≥ 1/2. The objective is to study asymptotic properties of the maximum likelihood estimator as the number of the Fourier ...

Parameter estimation for stochastic equations with additive fractional Brownian sheet

We study the maximum likelihood estimator for stochastic equations with additive fractional Brownian sheet. We use the Girsanov transform for the twoparameter fractional Brownian motion, as well as the Malliavin calculus and Gaussian regularity theory. Mathematics Subject Classification (2000): 60G15, G0H07, 60G35, 62M40

Parametric Estimation for Linear Stochastic Delay Differential Equations Driven by Fractional Brownian Motion

Consider a linear stochastic differential equation dX(t) = (aX(t) + bX(t− 1))dt+ dW t , t ≥ 0 with time delay driven by a fractional Brownian motion {WH t , t ≥ 0}. We investigate the asymptotic properties of the maximum likelihood estimator of the parameter θ = (a, b).

Parametric estimation for linear stochastic differential equations driven by fractional Brownian Motion

We investigate the asymptotic properties of the maximum likelihhod estimator and Bayes estimator of the drift parameter for stochastic processes satisfying a linear stochastic differential equations driven by fractional Brownian motion. We obtain a Bernstein-von Mises type theorem also for such a class of processes.

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion